Aircraft: B757
Phase of flight: taxi
Anomaly: Aircraft Equipment Problem Critical; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter Fuel Issue; Inflight Event / Encounter Weather / Turbulence

This flight was to be the last of a week long assignment of flying; and incorporated a schedule revision which resulted in a shift from day into evening flying to night into day flying. This shift could have been a factor in our one procedural omission. After a deadhead in; followed by approximately two hours of wait time; the subject flight commenced. Upon initial arrival at the aircraft; weather was IFR; but deteriorated somewhat rapidly to low IFR upon pushback. I then suggested a takeoff alternate with this development; which we obtained. What followed was a very challenging duty period. Initial taxi out ultimately was a low RVR taxi; involving multiple Sid/runway changes and high workload. The taxi out was exceptionally slow; with high vigilance for orientation; as well as other potential traffic. While we awaited sufficient takeoff minimums; a release revision for TO fuel became necessary; followed by a required [60% 10 second] engine runup [ice]. Each was accomplished. Coordination was ongoing with Dispatch and Operations for numerous evolving matters. Ultimately; we returned to the ramp due to expired holdover time; and the concurrent need for fuel upload. Taxi back in was below TO minimums; and took considerable time and care. Upon refueling; and a protracted de/anti ice process; weather improved to about 2 NM visibility; with no precipitation. The decision was made to return the fuel load to the original release fuel for various reasons.Taxi out was much easier this time; with generally good visibility. We noticed a long line of aircraft waiting to takeoff; so we shut down one engine during taxi; to avert a release fuel issue re-emerging. Shortly before takeoff; we restarted the right engine utilizing crossbreed thrust from the left engine. At this point we were number one for takeoff; and given takeoff clearance. With the drastically improved weather; we failed to accomplish a second static runup prior to takeoff. In retrospect; I believe a component of this was the accomplishment of the second engine re-start right before takeoff; and the associated checklists thereafter....a seldom utilized practice. During the takeoff roll; and in the low speed regime; but near takeoff thrust; the left engine compressor stalled; requiring an aborted takeoff; and return to the ramp for maintenance action. We were subsequently told by Maintenance that a valve or valves had coded as not sequencing properly; and that the engine had 'burped'. First attempt to depart resulted in a 1 + 46 turn back due to expired hold over time when visibility dropped from 2 1/2 SM to RVR 300 - 400. During our wait we had performed a 60% 10 second run-up (B757RR) holding short of runway. Then returned to ramp. After re-fueling we were pushed back for a second de-ice/anti-ice treatment which took a very long time during which wx improved to 1 1/2 SM and the sun was well up (negating the need for anti-ice; but it was already completed). On Taxiway Foxtrot I could see a long line of aircraft waiting on the taxiway for departure; so we decided to shut down the right engine to save fuel and avoid another delay (first taxi out required a new release to adjust takeoff fuel and we were number one for departure and couldn't risk shutting down an engine at that time). When we were #4 we restarted the right engine via a left engine cross bleed start. Visibility had improved. We were instructed to line up and wait; then cleared for take off. The First Officer was pilot flying and pushed the thrust levers up toward 60%; but neither one us had thought to hold it for 10 seconds prior to selecting N1 on the MCP. Shortly after selecting N1 on the MCP; and before reaching 60 KIAS; we heard a bang sound and the airplane made a slight jerk to the left. I rejected the take off and noted a burned rubber smell. I initially thought we might have blown a tire. After clearing the runway the First Officer asked ATC if anyone in the line of aircraft waiting for departure had noticed anything unusual during our brief takeoff roll. Some one answered they had seen a puff of black smoke from our left engine. We returned to the ramp for mx inspection and entered in the logbook as a suspected compressor stall. Maintenance confirmed a compressor stall and a code for a problem with a regulator valve. B757 flight crew describes a long morning which included deadheading into the trip two hours early; deicing; weather below minimums for takeoff; return to the gate for more fuel and more deicing; and ultimately a rejected takeoff due to a compressor stall.